The direction of arrival (DOA) estimation problem for sources with known waveforms in the presence of impulsive noise is studied. To solve the problem, the impulsive noise is decomposed into Gaussian and sparse parts, and a generalized ${\ell }_2-{\ell }_p$ minimization based cost function is developed by setting generalized Gaussian distribution (GGD) as the prior distribution of sparse part. Then, to solve this nonconvex problem, the generalized ${\ell }_2-{\ell }_p$ problem is decoupled into multiple independent and dimension reduced simple ${\ell }_2-{\ell }_p$ optimization problems with respect to the sparse part, and solved under the accelerated proximal gradient framework. Finally, DOAs and complex amplitudes are estimated from the cleaned data. As demonstrated by simulation results, the proposed method has a better performance than existing ones in the presence of Gaussian mixture model (GMM) and GGD noise, while it is comparable for symmetric $\alpha$ stable (S$\alpha$S) noise.

研究了在存在脉冲噪声的情况下具有已知波形的源的到达方向 (DOA) 估计问题。为解决该问题，将脉冲噪声分解为高斯部分和稀疏部分，并得到一个广义的${\ell }_2-{\ell }_{磷}$通过将广义高斯分布（GGD）设置为稀疏部分的先验分布来开发基于最小化的成本函数。然后，为了解决这个非凸问题，广义的${\ell }_2-{\ell }_{磷}$ 问题解耦为多个独立的，降维的简单 ${\ell }_2-{\ell }_{磷}$关于稀疏部分的优化问题，并在加速近端梯度框架下解决。最后，根据清洗后的数据估计 DOA 和复振幅。仿真结果表明，在存在高斯混合模型（GMM）和 GGD 噪声的情况下，所提出的方法比现有方法具有更好的性能，而对于对称$\alpha$ 稳定 (S$\alpha$S) 噪音。